Mathematics: Relations Functions Sets: Objectives and Representation of a Set

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Objectives

  • Define a set and represent the same in different forms.

  • Define different types of sets such as, finite and infinite sets, empty set, singleton set, equivalent sets, equal sets, subsets and cite examples thereof.

  • Define and cite examples of universal set, complement of a set and difference between two sets.

  • Define union and intersection of two sets.

  • Represent union and intersection of two sets, universal set, complement of a set, difference between two sets by Venn Diagram.

Venn Diagram

Venn Diagram

Venn Diagram

Some Standard Notations

Some standard notations to represent sets:

  • The set of natural numbers

  • The set of whole numbers

  • The set of integers

  • : The set of positive integers

  • : The set of negative integers

  • The set of rational numbers

  • The set of irrational numbers

  • The set of real numbers

  • The set of complex numbers

Other frequently used symbols are:

  • : ‘belongs to’

  • : ‘does not belong to’

  • : There exists

  • : There does not exist.

Example:

is the set of natural numbers and we know that is a natural number but is not a natural number? It can be written in the symbolic form as and .

Representation of a Set

There are two methods to represent a set.

(I) Roster Method (Tabular Form)

In this method a set is represented by listing all its elements, separating them by commas and enclosing them in curly bracket.

If be the set of vowels of English alphabet, it can be written in Roster form as:

Example:

Write the following in Roster form.

Solution:

(II) Set-Builder Form

In this form elements of the set are not listed but these are represented by some common property.

Let be the set of vowels of English alphabet then can be written in the set builder form as:

Example:

Write the following in set-builder form:

Solution:

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